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Evaluating Density Forecasts

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  • Francis X. Diebold
  • Todd A. Gunther
  • Anthony S. Tay

Abstract

We propose methods for evaluating density forecasts. We focus primarily on methods that are applicable regardless of the particular user's loss function. We illustrate the methods with a detailed simulation example, and then we present an application to density forecasting of daily stock market returns. We discuss extensions for improving suboptimal density forecasts, multi-step-ahead density forecast evaluation, multivariate density forecast evaluation, monitoring for structural change and its relationship to density forecasting, and density forecast evaluation with known loss function.

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File URL: http://fic.wharton.upenn.edu/fic/papers/97/9737.pdf
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Bibliographic Info

Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 97-37.

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Date of creation: Aug 1997
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Handle: RePEc:wop:pennin:97-37

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  1. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October.
  2. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  3. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
  4. Jacob A. Mincer & Victor Zarnowitz, 1969. "The Evaluation of Economic Forecasts," NBER Chapters, in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 1-46 National Bureau of Economic Research, Inc.
  5. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
  6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  7. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  8. Christoffersen, Peter F & Diebold, Francis X, 1996. "Further Results on Forecasting and Model Selection under Asymmetric Loss," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 561-71, Sept.-Oct.
  9. repec:att:wimass:9710 is not listed on IDEAS
  10. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  11. Clemen, Robert T. & Murphy, Allan H. & Winkler, Robert L., 1995. "Screening probability forecasts: contrasts between choosing and combining," International Journal of Forecasting, Elsevier, vol. 11(1), pages 133-145, March.
  12. Jeremy Berkowitz & Lutz Kilian, 1996. "Recent developments in bootstrapping time series," Finance and Economics Discussion Series 96-45, Board of Governors of the Federal Reserve System (U.S.).
  13. Clements, M.P. & Hendry, D., 1992. "On the Limitations of Comparing Mean Square Forecast Errors," Economics Series Working Papers 99138, University of Oxford, Department of Economics.
  14. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  15. Granger, C.W.J. & Pesaran, H., 1996. "A Decision_Theoretic Approach to Forecast Evaluation," Cambridge Working Papers in Economics 9618, Faculty of Economics, University of Cambridge.
  16. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  17. Peter F. Christoffersen & Francis X. Diebold, 1997. "Cointegration and long-horizon forecasting," Working Papers 97-14, Federal Reserve Bank of Philadelphia.
  18. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(06), pages 808-817, December.
  19. repec:cup:etheor:v:13:y:1997:i:6:p:808-17 is not listed on IDEAS
  20. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-44, April.
  21. West, Kenneth D & McCracken, Michael W, 1998. "Regression-Based Tests of Predictive Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 817-40, November.
  22. Campbell, Bryan & Ghysels, Eric, 1995. "Federal Budget Projections: A Nonparametric Assessment of Bias and Efficiency," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 17-31, February.
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